Gravitational Radiation and the Equivalence Principle by the Technique of Virtual Quanta

After reviewing the Weizsächer-Williams technique of virtual quanta for calculation of electromagnetic radiation in bremsstrahlung encounters, we extend the method to the domain of gravitational encounters and set up a correlation between collision problems and the corresponding problem of the generation of gravitational radiation. In the local rest frame of a relativistic test particle the gravitational field of a large mass consists predominantly of a pulse of plane—fronted gravitational waves. We Fourier—analyse this equivalent pulse and consider the scattering of the individual frequency components, virtual quanta, by the test body. The scattering occurs because of the long—range Newtonian field which gives a Rutherford—like cross section. The escape of this radiation to infinity, suitably transformed, gives us the radiative loss of gravitational energy by a rapidly moving particle. The radiation spectrum and total energy radiated are computed as an example. We then turn to the case where one or both of the masses possess an electric charge, and calculate the total electromagnetic and gravitational energy radiated in such encounters. We consider both the case in which the deflection is principally electromagnetic in nature, and the case in which the deflection is principally gravitational. The results are interpreted by considering the predictions of the equivalence principle, for the behavior of the test particle, and for the behavior of the virtual quanta. As expected from the equivalence principle, the total radiation produced is larger for electromagnetic deflection than for gravitational deflection through the same angle